Finite Group Databasebeta

← C4×#14556623 #22618751

Subgroups — C4×#14556623 #22618751

Order 9344.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556623C211yesmaximal, characteristic
2C4×#11924029C211yesmaximal, characteristic
3C4×Q8×D73C211yesmaximal, characteristic, complemented
4#17988694C211yesmaximal, characteristic, complemented
5#17988691C211yesmaximal, characteristic, complemented
6#17988690C211yesmaximal, characteristic, complemented
7#17988686C211yesmaximal, characteristic, complemented
8C4×#11924018C211yesmaximal, characteristic, complemented
9C4×#11924017C211yesmaximal, characteristic, complemented
10C4×#11924015C211yesmaximal, characteristic, complemented
11#17988628C211yesmaximal, characteristic, complemented
12#17988594C211yesmaximal, characteristic, complemented
13#17988587C211yesmaximal, characteristic
14C4×#11924011C211yesmaximal, characteristic, complemented
15C4×Q16×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18#14556623C418yesdirect product factor
19C2×#11924018C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924015C2211yescharacteristic
22C2×#11924011C2211yescharacteristic
23C2×#11924011C2211yescharacteristic
24Q8×Dic73C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic
26C4×Dic146—21no—
27C4×Dic146C2211yescharacteristic
28#14556556—21no—
29#14556556C2211yescharacteristic
30C4×D292—21no—
31C4×D292C2211yescharacteristic
32#14556553—21no—
33#14556553C2211yescharacteristic
34#14556549—21no—
35#14556549C2211yescharacteristic
36C4⋊C4×D73—21no—
37C4⋊C4×D73C2211yescharacteristic
38C42×D73—21no—
39C42×D73—21no—
40C42×D73C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556501C2211yescharacteristic
51#14556501C2211yescharacteristic
52C4×#10596831C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C4×Q8×C73C2211yescharacteristic
55C4×Q8×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C4×C8×C73C2211yescharacteristic
60#11924029—22no—
61#11924029C2×C414yes—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64Q8×D73—22no—
65Q8×D73C2×C414yescomplemented
66C2×D292—21no—
67C2×D292C2311yescharacteristic
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73D411yescharacteristic
74C2×C4×D73D411yescharacteristic
75C2×C4×D73C2311yescharacteristic
76#11924018C2×C414yescomplemented
77#11924017C2×C414yescomplemented
78#11924015C2×C414yescomplemented
79#11924011—22no—
80#11924011C2×C414yescomplemented
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73D411yescharacteristic
99C4×Dic73D411yescharacteristic
100C4×Dic73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C2×Q8×C73C2311yescharacteristic
103Q16×C73C2×C414yescomplemented
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73—21no—
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C42×C73—21no—
111C42×C73—21no—
112C42×C73C2311yescharacteristic
113C22×D73—21no—
114C22×D73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73C22×C412yes—
118Q8×C73C22×C412yes—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132D292—24no—
133D292—21no—
134D292C22×C412yes—
135C4×D73—24no—
136C4×D73—22no—
137C4×D73—24no—
138C4×D73—41no—
139C4×D73—42no—
140C4×D73—42no—
141C4×D73—42no—
142C4×D73C22×C412yes—
143C4×D73#4112yes—
144Dic146—21no—
145Dic146—24no—
146Dic146C22×C412yes—
147C8×C73—21no—
148C8×C73C22×C412yes—
149#10596831—21no—
150#10596831C22×C412yes—
151C22×C73C22×D411yescharacteristic
152C2×D73—21no—
153C2×D73—21no—
154C2×D73—22no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73C4×D412yes—
158C4×C73—22no—
159C4×C73—22no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73#13712yescomplemented
164C4×C73C23×C411yescharacteristic
165C4×C73C2×#4111yescharacteristic
166Dic73—22no—
167Dic73—21no—
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171Dic73C4×D412yes—
172C2×C73C2×C4×D411yescharacteristic
173C2×C73C2×#13711yescharacteristic
174C2×C73#57511yescharacteristic
175D73—22no—
176D73—42no—
177C4×#137—731nomaximal, Sylow
178C73C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—731no—
180C4×#41—731no—
181C2×C4×Q8—731no—
182#441—731no—
183#441—731no—
184#440—731no—
185#440—731no—
186C4×Q16—731no—
187C4×Q16D7311yescharacteristic, complemented
188C4×SD16—731no—
189C4×SD16—731no—
190#428—731no—
191#419—731no—
192#417—731no—
193C4×M16—731no—
194C2×#41—731no—
195C22×Q8—731no—
196#137—738no—
197C2×Q16—731no—
198C2×Q16C2×D7311yescharacteristic
199C2×SD16—731no—
200C2×SD16—731no—
201C2×M16—731no—
202C2×M16—731no—
203C4×Q8—731no—
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8—731no—
207C4×Q8—1461no—
208C4×Q8—1461no—
209C4×Q8C2×D7311yescharacteristic
210C4×Q8C2×D7311yescharacteristic
211C4×D4—731no—
212C4×D4—731no—
213C4×D4—1461no—
214C4×D4—1461no—
215#117—731no—
216#117—1461no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—1461no—
219C2×C42—731no—
220C2×C42—1461no—
221C2×C42—1461no—
222#107—731no—
223#107C2×D7311yescharacteristic
224#106—731no—
225#106—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103C2×D7311yescharacteristic
231#103C2×D7311yescharacteristic
232#102—731no—
233#102—731no—
234#97—731no—
235#97—731no—
236C4×C8—731no—
237C4×C8C2×D7311yescharacteristic
238#41—734no—
239#41—1462no—
240C2×Q8—734no—
241C2×Q8—731no—
242C2×Q8—1461no—
243C2×Q8—1462no—
244C2×Q8C22×D7311yescharacteristic
245C2×Q8C22×D7311yescharacteristic
246C2×D4—731no—
247C2×D4—1461no—
248C22×C4—731no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256Q16—734no—
257Q16C4×D7314yescomplemented
258SD16—734no—
259SD16—734no—
260M16—734no—
261M16—1462no—
262C2×C8—731no—
263C2×C8—731no—
264C2×C8C22×D7311yescharacteristic
265C2×C8C22×D7311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4C22×D7311yescharacteristic
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C42—21no—
281C42—21no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—1461no—
286C42—1461no—
287C42—1461no—
288C42—1461no—
289C42—1461no—
290C42C22×D7311yescharacteristic
291C23—731no—
292C23—1461no—
293Q8—21no—
294Q8—21no—
295Q8—732no—
296Q8—1464no—
297Q8—1461no—
298Q8C2×C4×D7312yes—
299Q8C2×C4×D7312yes—
300D4—732no—
301D4—1464no—
302D4—1461no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2921no—
308C2×C4—2922no—
309C2×C4—2922no—
310C2×C4—2922no—
311C2×C4—731no—
312C2×C4—732no—
313C2×C4—732no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—1464no—
317C2×C4—1464no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1462no—
322C2×C4D4×D7311yescharacteristic
323C2×C4D4×D7311yescharacteristic
324C2×C4C23×D7311yescharacteristic
325C8—21no—
326C8—732no—
327C8—1461no—
328C8C2×C4×D7312yes—
329C22—2921no—
330C22—2921no—
331C22—732no—
332C22—1462no—
333C22—1461no—
334C22—1461no—
335C22C2×D4×D7311yescharacteristic
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—2921no—
342C4—2921no—
343C4—732no—
344C4—1461no—
345C4—1461no—
346C4—1462no—
347C4#1455662312yesdirect product factor
348C4C22×C4×D7311yescharacteristic
349C4#41×D7311yescharacteristic
350C2—2922no—
351C2—1462no—
352C2C4×D4×D7311yescharacteristic
353C2C2×#1455662311yescharacteristic
354C2#1798938411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC4×C73C23×C4
FrattiniC2×C4C23×D73
FittingC4×Q16×C73C2
socleC22×C73C22×D4
hypercenterC4×Q16D73
hypocenterC73C4×#137
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C4×Q8×D73C2semidirect
4. #17988694C2semidirect
5. #17988691C2semidirect
6. #17988690C2semidirect
7. #17988686C2semidirect
8. C4×#11924018C2semidirect
9. C4×#11924017C2semidirect
10. C4×#11924015C2semidirect
11. #17988628C2semidirect
12. #17988594C2semidirect
14. C4×#11924011C2semidirect
15. C4×Q16×C73C2semidirect
18. #14556623C4direct (N × H)
65. Q8×D73C2×C4semidirect
76. #11924018C2×C4semidirect
77. #11924017C2×C4semidirect
78. #11924015C2×C4semidirect
80. #11924011C2×C4semidirect
103. Q16×C73C2×C4semidirect
163. C4×C73#137semidirect
178. C73C4×#137semidirect
187. C4×Q16D73semidirect
257. Q16C4×D73semidirect
347. C4#14556623direct (N × H)